We consider here the fault detection and isolation (FDI) problem for linear systems. We are interested in designing a set of observer-based residuals, in such a way that the transfer from the faults to the residuals is diagonal and the transfer from the disturbances to the residuals is zero. We deal with this problem when the system under consideration is structured, that is, the entries of the system matrices are either fixed zeros or free parameters. This problem can be solved in terms of the graph that can be associated in a natural way with a structured system. When the FDI solvability conditions are not satisfied, we assume that internal variables can be measured at a cost and look into the question of wether the problem is solvable with these new measurements. We give solvability conditions for a solution with a minimal number of additional sensors and among such solutions provide a minimal cost solution for the sensor location problem under consideration. We pay particular attention to the internal analysis of the system, and we propose a structural decomposition of the system associated graph based on some particular separators. This analysis leads to the definition of a reduced system. We prove that some potential additional sensors are inefficient for solving our FDI problem and that the FDI problem can be solved using only measurements on the reduced system View full abstract»

In this paper, we study the human oculomotor system as a simple mechanical control system. It is a well known physiological fact that all eye movements obey Listing's law, which states that eye orientations form a subset consisting of rotation matrices for which the axes are orthogonal to the normal gaze direction. First, we discuss the geometry of this restricted configuration space (referred to as the Listing space). Then we formulate the system as a simple mechanical control system with a holonomic constraint. We propose a realistic model with musculotendon complexes and address the question of controlling the gaze. As an example, an optimal energy control problem is formulated and numerically solved View full abstract»

This paper focuses on the model reduction of nonstationary linear parameter-varying (NSLPV) systems. We provide a generalization of the balanced truncation procedure for the model reduction of stable NSLPV systems, along with a priori error bounds. Then, for illustration purposes, this method is applied to reduce the model of a two-mass translational system. Furthermore, we give an approach for the model reduction of stabilizable and detectable systems, which requires the development and use of coprime factorizations for NSLPV models. For the general class of eventually periodic LPV systems, which includes periodic and finite horizon systems as special cases, our results can be explicitly computed using semidefinite programming View full abstract»

The robust performance analysis problem is considered for linear time-invariant (LTI) systems subject to block-diagonal structured and bounded linear time-varying (LTV) perturbations with specified maximal rates-of-variation. Analysis methods are developed in terms of semidefinite programming for the computation of upper and lower bounds for the optimum robust performance level. The upper bound computation is based on an integral quadratic constraint (IQC) test developed using a generalized version of the so-called swapping lemma. The lower bound computation method employs an extended version of the power distribution theorem together with a generalized version of the Kalman-Yakubovich-Popov (KYP) lemma and serves as a means to assess the conservatism of the computed upper bounds in the case of dynamic LTV perturbations. As corollaries of the underlying result for lower bound computation, it is shown for general block-diagonal uncertainty structures that thefrequency-dependent/constant D-scaling tests are exact for robust performance analysis against arbitrarily slow/fast dynamic LTV perturbations, respectively View full abstract»

When a covariance matrix with a Toeplitz structure is written as the sum of a singular one and a positive scalar multiple of the identity, the singular summand corresponds to the covariance of a purely deterministic component of a time-series whereas the identity corresponds to white noise-this is the Caratheacuteodory-Fejeacuter-Pisarenko (CFP) decomposition. In the present paper we study multivariable analogs for block-Toeplitz matrices as well as for matrices with the structure of state-covariances of finite-dimensional linear systems (which include block-Toeplitz ones). To this end, we develop theory which addresses questions of existence, uniqueness and realization of multivariable power spectra, possibly having deterministic components. We characterize state-covariances which admit only a deterministic input power spectrum, and we explain how to realize multivariable power spectra which are consistent with singular state covariances via decomposing the contribution of the singular part. We then show that multivariable decomposition of a state-covariance in accordance with a "deterministic component + white noise" hypothesis for the input does not exist in general. We finally reinterpret the CFP-dictum and consider replacing the "scalar multiple of the identity" by a covariance of maximal trace which is admissible as a summand. The summand can be either (block-)diagonal corresponding to white noise or have a "short-range correlation structure" corresponding to a moving average component. The trace represents the maximal variance/energy that can be accounted for by a process at the input (e.g., noise) with the aforementioned structure, and this maximal solution can be computed via convex optimization. The decomposition of covariances and spectra according to the range of their time-domain correlations is an alternative to the CFP-dictum with potentially great practical significance View full abstract»

The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those encountered in the same kind of extension to linear dynamical systems over rings, it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings. Sufficient conditions are given for computing the maximal (A,B)-invariant subspace contained in a given space and the existence of linear state feedbacks is discussed. An application to the study of transportation networks which evolve according to a timetable is considered View full abstract»

A differential variational system is defined by an ordinary differential equation (ODE) parameterized by an algebraic variable that is required to be a solution of a finite-dimensional variational inequality containing the state variable of the system. This paper addresses two system-theoretic topics for such a nontraditional nonsmooth dynamical system; namely, (non-)Zenoness and local observability of a given state satisfying a blanket strong regularity condition. For the former topic, which is of contemporary interest in the study of hybrid systems, we extend the results in our previous paper, where we have studied Zeno states and switching times in a linear complementarity system (LCS). As a special case of the differential variational inequality (DVI), the LCS consists of a linear, time-invariant ODE and a linear complementarity problem. The extension to a nonlinear complementarity system (NCS) with analytic inputs turns out to be non-trivial as we need to use the Lie derivatives of analytic functions in order to arrive at an expansion of the solution trajectory near a given state. Further extension to a differential variational inequality is obtained via its equivalent Karush-Kuhn-Tucker formulation. For the second topic, which is classical in system theory, we use the non-Zenoness result and the recent results in a previous paper pertaining to the B-differentiability of the solution operator of a nonsmooth ODE to obtain a sufficient condition for the short-time local observability of a given strongly regular state of an NCS. Refined sufficient conditions and necessary conditions for local observability of the LCS satisfying the P-property are obtained View full abstract»

This paper employs dissipativity theory for the global analysis of limit cycles in particular dynamical systems of possibly high dimension. Oscillators are regarded as open systems that satisfy a particular dissipation inequality. It is shown that this characterization has implications for the global stability analysis of limit cycle oscillations: i) in isolated oscillators, ii) in interconnections of oscillators, and iii) for the global synchrony analysis in interconnections of identical oscillators View full abstract»

This paper is concerned with the finite horizon Hinfin full-information control for discrete-time systems with multiple control and exogenous input delays. We first establish a duality between the Hinfin full-information control and the H2 smoothing of a stochastic backward system in Krein space. Like the duality between the linear quadratic regulation (LQR) of linear systems without delays and the Kalman filtering, the established duality allows us to address complicated multiple input delay problems in a simple way. Indeed, by applying innovation analysis and standard projection in Krein space, in this paper we derive conditions under which the Hinfin full-information control is solvable. An explicit controller is constructed in terms of two standard Riccati difference equations of the same order as the original plant (ignoring the delays). As special cases, solutions to the Hinfin state feedback control problem for systems with delays only in control inputs and the Hinfin control with preview are obtained. An example is given to demonstrate the effectiveness of the proposed Hinfin control design View full abstract»

In this note, we consider a set up in which the plant and controller are local to each other, but are together driven by a remote reference signal that is transmitted through a noisy discrete channel. Our goal is to design codeword lengths of block source and channel encoders, and a controller to meet a model matching performance objective. Such design problems are difficult in general, as there is a strong interplay between control objectives and communication constraints, which forces the synthesis of controllers and encoder-decoder pairs to be done simultaneously. Current approaches typically fix one, while the other is designed to meet some objective. We first construct a model matching performance metric that captures the tradeoffs between coding the reference command to achieve more accuracy at the remote site and designing a controller to meet performance. We then simultaneously synthesize the controller and encoder codeword lengths that meet the specified objective for a first-order plant and model case. Finally, we illustrate performance sensitivity to the poles of the plant and model, and to the channel noise View full abstract»

The properties of a system, proposed by Teel and Hespanha, which is globally exponentially stable but with state that can be driven to infinity by an arbitrarily small exponentially decaying disturbance, are discussed in detail. These are used to propose a family of systems with a similar property and to argue that unstable behavior may be nongeneric and not detected by means of simulations. Finally, sufficient conditions for the existence of unbounded trajectories in cascaded systems are given View full abstract»

A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method View full abstract»

Processor-sharing queues are often used to model file transmission in networks. While sojourn time is a common performance metric in the queueing literature, average transmission rate is the more commonly discussed metric in the networking literature. Whereas much is known about sojourn times, there is little known about the average service rate experienced by jobs in processor-sharing queues. We first define the average rate as observed by users and by the queue. In an M/M/1 processor-sharing queue, we give closed-form expressions for these average rates, and prove a strict ordering amongst them. We prove that the queue service rate (in bps) is an increasing function of the minimum required average transmission rate, and give a closed-form expression for the marginal cost associated with such a performance requirement. We then consider the effect of using connection access control by modeling an M/M/1/K processor-sharing queue. We give closed-form expressions for average transmission rates, and discuss the relationship between the queue service rate (in bps), the queue limit, the average rate, and the blocking probability View full abstract»

This note addresses the problem of enforcing generalized mutual exclusion constraints on a Petri net plant. First, we replace the classical partition of the event set into controllable and uncontrollable events from supervisory control theory, by associating a control and observation cost to each event. This leads naturally to formulate the supervisory control problem as an optimal control problem. Monitor places which enforce the constraint are devised as a solution of an integer linear programming problem whose objective function is expressed in terms of the introduced costs. Second, we consider timed models for which the monitor choice may lead to performance optimization. If the plant net belongs to the class of mono-T-semiflow nets, we present an integer linear fractional programming approach to synthesize the optimal monitor so as to minimize the cycle time lower bound of the closed loop net. For strongly connected marked graphs the cycle time of the closed-loop net can be minimized View full abstract»

A new robust control gain-scheduling scheme for uncertain linear parameter-varying (LPV) systems is proposed. The gain-scheduled controller consists of a set of minimax optimal robust controllers and incorporates a new interpolation rule to achieve continuity of the controller gain over a range of operating conditions. For every fixed system parameter, the proposed controller guarantees a certain bound on the worst-case performance of the corresponding uncertain closed loop system. Furthermore, a bound on the rate of parameter variations is obtained under which the closed loop LPV system is robustly stable View full abstract»

This note considers position and attitude control of large space structures composed of a number of subsystems (substructures) interconnected by flexible links. A decentralized control law of dynamic displacement feedback compatible with subsystems is applied under the assumption that sensors and actuators are collocated. It has been known that the overall closed-loop system is robustly stable against uncertainties in mass, damping, and stiffness, if rigid modes of each subsystem are controllable and observable. The objective of this note is to derive conditions for the overall system to be stable even when some local controllers fail. The conditions are expressed in terms of the stiffness (or damping) matrices and interconnection location matrices of the subsystems whose local controllers fail View full abstract»

We consider the kinematic model of a car which describes the rolling-without-slipping constraint of the wheels on an horizontal floor and the bound on the angle of steering of front wheels. The problem of determining shortest paths for such a vehicle is known as the Reeds and Shepp's problem. Ten years ago, a complete solution to this problem was determined on the basis of a complex reasoning grounded on the necessary conditions of Pontryagin's Maximum Principle and completed with a set of geometric arguments. In this note, we provide a simple new proof of the optimality of this construction by using a verification theorem based on Boltianskii's sufficient regularity conditions. To our knowledge, it is the first example of a regular synthesis for a nonholonomic system in a three-dimensional space View full abstract»

This note is concerned with the stability analysis of discrete-time systems with time-varying state delay. By defining new Lyapunov functions and by making use of novel techniques to achieve delay dependence, several new conditions are obtained for the asymptotic stability of these systems. The merit of the proposed conditions lies in their less conservativeness, which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms Sigmam=k-dkk-1(middot) and Sigma m=k-dMk-1(middot), which is largely ignored in the existing literature. These conditions are shown, via several examples, to be much less conservative than some existing result View full abstract»

We present a method for constructing reduced-order state observers for linear systems with unknown inputs. Our approach provides a characterization of observers with delay, which eases the established necessary conditions for existence of unknown input observers with zero-delay. We develop a parameterization of the observer gain that decouples the unknown inputs from the estimation error, and we use the remaining freedom to ensure stability of the error dynamics. Our procedure is quite general in that it encompasses the design of full-order observers via appropriate choices of design matrices View full abstract»

In this note, we show that min-max model predictive control (MPC) for linearly constrained polytopic systems with quadratic cost can be cast as a quadratically constrained quadratic program (QCQP). We use the rigorous closed loop formulation of min-max MPC, and show that any such min-max MPC problem with convex costs and constraints can be cast as a finite dimensional convex optimization problem, with the QCQP arising from quadratic costs as a special case. At the base of the proof is a lemma showing the convexity of the dynamic programming cost-to-go, which implies that the worst case on an infinite polytopic set is assumed on one of its finitely many vertices. As the approach is based on a scenario tree formulation, the number of variables in this problem grows exponentially with the horizon length. Fortunately, the QCQP is tree structured, and can thus be efficiently solved by specially tailored interior-point methods whose computational costs are linear in the number of variables. The new formulation as a tree sparse QCQP promises to facilitate online solution of the rigorous min-max MPC problem with quadratic costs View full abstract»

This note presents a robust moving horizon Hinfin control scheme that achieves disturbance attenuation with performance adaptation or for a prescribed level. The on-line solved optimization problem is a Lagrange relaxation of the constrained minimax problem, with the benefit of achieving feasibility in the moving horizon implementation. Uncertainties are incorporated by the use of the full block multiplier technique. Simulation and comparison results are given View full abstract»

Using the correlated properties between the diagonal element and the singular value of the matrix, we propose new trace bounds for the product of two arbitrary real square matrices and improve the recent results View full abstract»

Aims & Scope

In the IEEE Transactions on Automatic Control, the IEEE Control Systems Society publishes high-quality papers on the theory, design, and applications of control engineering. Two types of contributions are regularly considered